Question

If a and ß are the roots of the equation x2 - 4x + 1 = 0, find (i) alpha square + Beta square (2) alpha/beta+beta/alpha​

Answer 1

Answer:

Using formula that

product of roots of an equation ax^2 +bx+c=0

=c/a

and some of its roots is -b/a.

As roots

roots of

${x}^{2} - 4x + 1=0$

are α and β

αβ (product of roots ) =1

α+β (sum of roots )= 4

Now

i)

${ \alpha }^{2} + { \beta }^{2}$

=${( \alpha + \beta )}^{2} - 2 \alpha \beta$

put values α+β and αβ

${2}^{2} - 2 \\ 4 - 2 \\ = \boxed{ \boxed{2}} \: \: \: \: \: \: \: \: \: \: \boxed{ \boxed{answer}}$

Now

ii)

$\frac{ \alpha }{ \beta } + \frac{ \beta }{ \alpha } \\ = \frac{ { \alpha }^{2} + { \beta }^{2} } { \alpha \beta }$

$put \: values \: of \: { \alpha }^{2} + { \beta }^{2} \\ and \: \alpha \beta$

$\implies \: \frac{ { \alpha } ^{2} + { \beta }^{2} }{ \alpha \beta } = \frac{2}{1} \\ = \boxed{ \boxed{2}} \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \boxed{answer}} \:$

Answer 2

Answer:

The roots of the equation = x^2 - 4x +1= 0.

= The sum of Roots of equation = 4.

= The product of Roots of equation = 1.

(i). = a^2 + B^2

= (a + B^2) - 2aB

The value a + B and aB:

= 2^2 - 2

= 4 - 2

= 2

(ii). = a. + B

B. a

= a^2 + B^2

aB

The value of a^2 + B^2 and aB:

=. a^2 + B^2 = 2

aB. 1

= 2

1

= 2